Conventional door opening and closing apparatus for a vehicle include a door handle attached to a vehicle door, with a space defined by a recess provided in the vehicle door located at the back of a gripper of the door handle. A user inserts his hand into the space to put his finger tip on the back of the grip. That is, the space allows gripping of the door handle by the user. This apparatus includes an injection nozzle that faces the back of the gripper opposing the space. Air injected from the injection nozzle blows off rain drops attached to the back of the gripper to clear the back of the grip. This prevents the user's finger tip from getting wet in contacting the back of the gripper. For example, see Patent Document 1.    Patent Document 1: Japanese Laid-open Patent Publication No. 2007-146593.
However, in the door opening and closing apparatus for a vehicle of Patent Document 1, an injection nozzle that injects air is required to blow off rain drops attached to the back of the grip of the door handle. In addition, an additional pipe or a fan is necessary to feed air into the injection nozzle. This adds to the number of required parts for the apparatus, and is disadvantageous with respect to cost. Space for placing the injection nozzle is required in the vehicle door, which is less practical.